Optica Applicata, Vol. LI, No. 3, 2021

DOI: 10.37190/oa210301

Bend loss fiber optics design based on sinusoidal and ellipse configurations

NOOR AZIE AZURA MOHD ARIF1*, DILLA DURHYA BURHANUDDIN2, SAHBUDIN SHAARI2, ABANG ANNUAR EHSAN2

1Centre for Pre-University Studies, Universiti Malaysia Sarawak, 94300 Kota Samarahan, Sarawak, Malaysia

2Institute of Microengineering and Nanoelectronics (IMEN), Universiti Kebangsaan Malaysia (UKM), 43600 Bangi, Malaysia

*Corresponding author: manaazura@unimas.my, aaehsan@ukm.edu.my

Bending losses in optical fibers comprise one of the extrinsic attenuations that contribute to opticalloss and they are essential for optical fiber bending sensor applications. This work investigatedthe optical loss in a standard single-mode step-index fiber optics due to fiber bending at 1550 nmwavelength. Variations in macro-bending loss with curvature radius and turn number have beenmeasured. Curvature radius and turn number are examined for sinusoidal and elliptical shapedbending configurations. It has been found that the loss increases as the bending radius and numberof turns increase. The result also showed that elliptical shaped bending configuration producedmore loss in contrast to that of sinusoidal shaped at bending angles of 180° and 360°. The studyon the macro-bending loss in terms of curvature radius and turn number for both elliptical and si-nusoidal shaped bending configurations is beneficial for future fiber optic sensor applications.

Keywords: sinusoidal shape, ellipse shape, bending loss, number of turns, curvature radius.

1. Introduction

Light loss mechanism in an optical fiber can be related to the transmission, reflectionand refraction of light [1]. Attenuation mechanism can be grouped into two attenuationcategories, namely intrinsic and extrinsic attenuation. Substances that are present inthe fiber optics as impurities contribute to intrinsic attenuation. Imperfection in theglass is another example that contributes to intrinsic attenuation. Both examples arecaused by the properties of the fiber and these impurities and imperfection can besolved with a more accessible technique compared with extrinsic attenuation. Extrinsicattenuation is caused by external forces [2]. Macro- and micro-bending are techniquesin which loss can be affected by one of these techniques. Generally, losses in an opticalfiber are not desired for telecommunication applications but it can be valuable for op-tical fiber bending sensor applications. Macro- and micro-bending designs are designconfigurations that can provide effective loss control mechanism in fiber bending sen-

310 N.A.A. MOHD ARIF et al.

sors. Numerous fiber bending sensors have been proposed to measure different phys-ical parameters such as voltage, pressure, strain, temperature [3–5]. At present, thebending loss mechanism is being used in wearable sensors for respiration and heartbeatdetection.

Micro-bend loss is due to microscopic fiber deformation in the core-cladding inter-face in which bending is caused by a small radius of curvature [2, 6]. Macro-bends arebends on the fiber with the radius of the curve being much higher than the radius ofthe fiber, which can be denoted as r >> a where a is the core radius and r is the radiusof curvature. Commonly, macro-bends can be described by a bend angle and bend ra-dius. Basically, light is not confined and guided in the fiber optics core when the fiberis bent. Total internal reflection of light propagating in the core at the core-claddinginterface will fail when light propagates at an angle higher than the critical angle. Nowa-days, several approaches to bending loss have been explained using different fiberbending configurations, including single loop, U-shape, sinusoidal and figure-of-eightshapes [1]. In this article, the study on the relationships between macro-bending lossand bending radius and between macro-bending loss and turn number for sinusoidaland elliptical bending configurations is conducted. Different radius of curvature andturn numbers have been considered to investigate their effect on bending loss.

2. Theoretical study

A single-mode with length l, and general bending loss L for a single-mode is usuallyobtained by [1, 6–10]

(1)

where α is the bending loss coefficient, and it is a function of bending radius, lightwavelength and optical fiber material and structure.

2.1. Bending radius

According to [6, 8], the bending loss with various bending radii R is

(2)

where ηR1 and ηR2

are fitting parameters. This formula was generated using fixed pa-rameters, namely, bending angle θ, wrapping turn N and wavelength λ.

2.2. Turns number

Bending loss with different turn numbers at the same value of wavelength can simplifythe relationship as a linear equation

LN = ηN N (3)

where LN is the loss due to the number of turns N. In addition to being simple, this linearequation is practical and thus is suitable and valid for a larger radius of curvature [6, 8].

Ls 10 e2α l log 8.686αL= =

LR ηR1ηR2

– R exp=

Bend loss fiber optics design... 311

2.3. Configuration of fiber bending

Guidance of light traveling through standard single-mode fiber SMF-28e+ can be re-lated and discussed using the phenomenon of total internal reflection (TIR). Although,ray-tracing analysis usually is used when the size of the fiber or waveguide region is muchlarger than the wavelength which is more practical in multimode fiber optics. However,this theory is used only proves that the loss between two configurations of fiber opticsdesign. The propagation of light in half-turn of ellipse, sinusoidal and ellipse shapesare discussed.

2.3.1. Propagation of light for the U-shape or half turn of the ellipse shape

In the sensing region, with U-shape configuration (Fig. 1), the angle of a ray with thenormal to the core-cladding interface should be greater than the critical angle. Withthis situation, the ray is capable of propagating through the sensing part. If θ representsthe angle that a guided ray makes with the normal to the core-cladding interface in thestraight fiber, then the corresponding angle φ at the outer surface of the bent-core isgiven by the expression done by [11–13]:

(4)

where h is the distance at which the ray is incident on the entrance of fiber from thecore-cladding boundary B is the bending radius, and w is the waveguide width. Simi-larly, angle δ of the ray at the inner surface of the bent-core is given by:

(5)

Fig. 1. Meridional ray in U-shaped or half-turn of ellipse shape sensing region.

φsinB h+B w+

-------------------- θsin=

δsinB h+

B----------------- θsin=

312 N.A.A. MOHD ARIF et al.

Thus, the angle θ is transformed to angle φ and δ. Hence, φ1 and φ2 for the outersurface can be written as:

and (6)

Similarly, for the inner surface of the sensing region it can be written as:

and δ2 = 90° (7)

2.3.2. Propagation of light for the sinusoidal shape

Sinusoidal shapes can be explained by adding one more U-shape but in the oppositedirection (180°) as shown in Fig. 2. The angles at the first bend can be explained byEqs. (6) and (7). This explanation was done by [13] but at S-shaped waveguide. Hence,

φ1 sin 1– B h+ ncladding

B w+ ncore

-----------------------------------------= φ2 sin 1– B h+B w+

------------------=

δ1 sin 1– B h+ ncladding

B ncore

-----------------------------------------=

Fig. 2. Meridional ray in the sinusoidal shape sensing region.

Bend loss fiber optics design... 313

by understanding the way of calculation, the range of the angle of incidence at the firstbend changes the angle at the second bend, and it can be written as:

(8)

(9)

Then,

(10)

(11)

where w is the waveguide width, B' is the bending radius of the second bend and h' isthe ray’s entrance height from the first bend to the second bend.

2.3.3. Propagation of light for an ellipse shape

The range of the angle of incidence at the first bend in an ellipse shape, as shown inFig. 3, can be explained by previous equations that are modified by [13] for the spiralwaveguide. Furthermore, the range of the angle of incidence with the normal to thecore-cladding interface at the first bend changes and values of the angle of incidenceat the second bend can be calculated as follows:

φ'1 sin 1– B w+B' w+

--------------------B' w h'–+ ncladding

B' w+ ncore

-------------------------------------------------------=

φ'2 sin 1– B w+B' w+

-------------------- B' w h'–+B' w+

-------------------------------=

δ'1 sin 1– B' w+B'

------------------- B w+B' w+

--------------------B' w h'–+ ncladding

B' w+ ncore

-------------------------------------------------------=

δ'2 sin 1– B' w+B'

-------------------- B w+B' w+

-------------------- B' w h'–+B' w+

--------------------------------=

Fig. 3. Meridional ray in ellipse shape sensing region.

314 N.A.A. MOHD ARIF et al.

(12)

(13)

then,

(14)

(15)

Owing to the configuration of the bending fiber, the partial loss of these propagatingrays at the outer (Lo) or inner (Li) bend surface due to each of the TIRs is as follows:

or (16)

where Lo or Li is the partial loss of optical power, λ is the wavelength, α is the bulk-at-tenuation coefficient at the region of contact, n2 is the refractive index at the boundaryand θcc is the critical angle, where

(17)

and ψ = 90° – φ or ψ = 90° – δ, φ and δ being the angle of incidence of light on theinterface at the bent outer and inner sensing regions. Then, the number of ray reflectionsper unit length at each outer (No) or inner (Ni) bend surface of the sensing region canbe written as:

or (18)

Hence, the loss of optical power per unit length LN can be determined by multiplyingthe corresponding L and N values for the inner and outer bend surfaces,

LN = Lo × No or LN = Li × Ni (19)

3. Method

In this experiment, measurements were conducted using standard single-mode opticalfiber (Corning SMF-28e+) with core and cladding diameters of 9 and 125 μm, respec-tively. Considering the refractive index of core and cladding to be 1.4645 and 1.456,respectively. The optical fiber of the sinusoidal shape of different vertices as shown

δ'1 sin 1– B w+B h'+

-------------------B' h'+ ncladding

B' ncore

---------------------------------------------=

δ'2 sin 1– B w+B h'+

------------------- B' h'+B'

---------------------=

φ'1 sin 1– B'B' w+

-------------------- B w+B h'+

-------------------B' h'+ ncladding

B' ncore

--------------------------------------------=

φ'2 sin 1– B'B' w+

-------------------- B w+B h'+

------------------- B' h'+B'

--------------------=

Lo

4 ψ /θcc2

θcc2 ψ2–

------------------------------ λα4πn2

----------------

= Li

4 ψ /θcc2

θcc2 ψ2–

------------------------------ λα4πn2

----------------

=

θccπ2

------ sin1– n2

n1

---------

– cos1– n2

n1

---------

= =

Noφcot

2w---------------= Ni

δcot2w

--------------=

Bend loss fiber optics design... 315

T a b l e 1. Fiber optics configurations with detailed parameters.

Shape Wavelength [nm] Tip vertex a [cm] Lateral vertex b [cm]

Sinusoidal/ellipse

1550

2.5 0.75

2.0 0.75

1.5 0.75

1.0 0.75

Fig. 4. Radius r of the circle in an ellipse with tip vertex a and lateral vertex b of ellipse.

N turns

Optical

Bending fiber

Wavelength tunablelight output (1550 nm)

Wavelength tunablelight output (1550 nm)

(sinusoidal shape)

Bending fiber(sinusoidal shape)

Optical

N turns

Fig. 5. Schematic diagram of the optical set-up for measuring bending loss of the fiber.

power meter

power meter

316 N.A.A. MOHD ARIF et al.

in Table 1 was made and used for the bent fiber with the input of the power meter op-erating at the wavelength of 1550 nm. An ellipse shape was bent with a double sinu-soidal shape, which can be explained in Fig. 4. To study the effect of the number ofturns (N ) on bending loss, up to 6 turns were investigated. A schematic diagram of theset-up for measuring the bending loss is shown in Fig. 5.

4. Results and discussion

For investigating the essential characterization of bending loss, the effect of bendingradius R was studied and then the influence of turns number N on the loss was inves-tigated.

4.1. Effect of bending radius

When the fiber is bent at less than 0.15 cm, the bending loss will increase rapidly, asshown in Fig. 6. Thus, it is observed that a larger bending radius will induce a higher

Fig. 6. Relationship between bending radius and bending loss: (a) sinusoidal shape, and (b) ellipse shape.

N = 1N = 2N = 3N = 4N = 5N = 6

26

22

18

14

10

6

2

55

50

45

40

35

30

25

20

15

10

5

00.10 0.15 0.20 0.25 0.30 0.35

Be

nd

loss

[d

B]

Radius [cm]

a

b

N = 1N = 2N = 3N = 4N = 5N = 6

Be

nd

loss

[d

B]

Bend loss fiber optics design... 317

bending loss. The variation shows an exponentially varying curve that satisfies theproposed relationship between losses and curvature radius by [14, 15]. Tip and lateralvertices effect the bending radius. The radius of the circle within the ellipse can be ob-tained according to the general formula of the ellipse base.

4.2. Influence of turns number

The bending losses from 1 to 6 turns in 1550 nm wavelength with various bendingradiuses are measured in this section. The experimental results, as shown in Fig. 7,show that the relationship between bending loss LN and turn number N can be simpli-fied as a linear equation for both fiber configurations satisfying the proposed relation-ship between losses and number of turns in [2, 14]. By considering and comparisonwith the general single-mode bending loss [1, 6, 7], the following relationships can bedetermined:

B = 8.686α l (20)

And l can be calculated using

for a sinusoidal shape, and (21)

for an ellipse shape (22)

where a and b are tip vertex and lateral vertex of an ellipse, respectively.As can be seen from Fig. 7, variations of L against N plotted for both configurations

show that the lower bend loss occured when the lateral vertex of sinusoidal shape is2.5 cm. Both values of semi-axes of the ellipse are essential to determining the sensi-tivity of fiber optics on the bend loss effect. Ellipse is considered in this situation be-

Fig. 7. Variation of bending loss versus a number of turns: (a) sinusoidal shape, and (b) ellipse shape.

Bend loss 2.5 × 1.5 sinusoidal60

50

40

30

20

10

0

0 1 2 3 4 5 6

Be

nd

ing

loss

[d

B]

Number of loop N

Bend loss 2.0 × 1.5 sinusoidalBend loss 1.5 × 1.5 sinusoidalBend loss 1.0 × 1.5 sinusoidalBend loss 2.5 × 1.5 ellipseBend loss 2.0 × 1.5 ellipseBend loss 1.5 × 1.5 ellipseBend loss 1.0 × 1.5 ellipse

lπ2

------ 3 a b+ 3 a b+ a 3b+ –=

l π 3 a b+ 3 a b+ a 3b+ –=

318 N.A.A. MOHD ARIF et al.

cause the changes of amplitude and period on sinusoidal shape affect the geometry ofthe bend-like elliptical shape. As seen in Table 2, a change in loop periodicity is in-versely proportional to changes in loop amplitudes. The most sensitive sensing regionhas a more significant parameter of sensor sensing sensitivity, and the sensitivity S canbe related as

(23)

where a and b are the tip and lateral vertices of an ellipse, respectively. This sensitivitycan be applied for both shapes due to the relation shape of the fiber optic design.

4.3. Influence of refractive index

Figures 6 and 7, indicated that losses are higher in elliptical shape configuration. Thisphenomenon can be related to the behaviour of light propagation into the sensing regiondue to fiber bending, as discussed in the theoretical part that is influenced by a fiberoptic refractive index. The loss of optical power was calculated at the fixed values ofw, ε, λ and θcc using Eq. (19). The values of power loss for sinusoidal and ellipticalshapes of fiber optics configurations are 3.34 × 10–7 and 3.23 × 10–6 W, respectively.This result shows that elliptical shape fiber optics configuration generated higher lossthan that of sinusoidal shape fiber optics configuration. Different values of core andcladding of the refractive index were examined as shown in Table 3 and it confirmedthat higher loss was generated in ellipse shape due to the total internal reflection.

5. Conclusion

The effect of bending radius and turn number on bending loss in step-index fiber opticshas been investigated. This study showed that bending loss decreases as curvature ra-

T a b l e 2. Sensitivity according to changes in loop.

Tip vertex a [cm] Lateral vertex b [cm] Sensitivity

2.5 0.75 1.8257

2.0 0.75 1.6330

1.5 0.75 1.4142

1.0 0.75 1.1547

S ab

-------=

T a b l e 3. Loss due to different refractive indexes.

ncore ncladding Loss in sinusoidal shape [W] Loss in ellipse shape [W]

1.45000 1.44470 3.40 × 10–7 3.25 × 10–6

1.46770 1.46280 3.83 × 10–7 3.20 × 10–6

1.44940 1.44400 3.36 × 10–7 3.26 × 10–6

1.46165 1.45600 3.37 × 10–7 3.23 × 10–6

1.46145 1.45600 3.34 × 10–7 3.30 × 10–6

Bend loss fiber optics design... 319

dius and turns number decrease. Furthermore, the type of configurations of fiber bend-ing, either a sinusoidal or elliptical shape also affects the bending loss. Elliptical shapegenerated higher loss than did sinusoidal shape. By analyzing the relationship betweenbending loss and bending radius and turn number, it is found that a single-mode opticalfiber has potential in fiber optics sensor application due to higher sensitivity on bend-ing loss.

Acknowledgements – Author are thankful to Nanophotonics Lab, Institute of Microengineering andNanoelectronics (IMEN), UKM for providing facilities. Financial support from the Ministry of HigherEducation (MOHE) and Universiti Malaysia Sarawak are gratefully acknowledged.

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Received April 22, 2020in revised form July 20, 2020